Optical communications systems typically include a pair of network nodes connected by an optical waveguide (i.e., fiber) link. Within each network node, communications signals are converted into electrical signals for signal regeneration and/or routing, and converted into optical signals for transmission through an optical link to another node. The optical link between the network nodes is typically made up of multiple concatenated optical components, including one or more (and possibly 20 or more) optical fiber spans (e.g., of 40-150 km in length) interconnected by optical amplifiers.
The use of concatenated optical components within a link enables improved signal reach (that is, the distance that an optical signal can be conveyed before being reconverted into electrical form for regeneration). Thus, for example, optical signals are progressively attenuated as they propagate through a span, and amplified by an optical amplifier (e.g., an Erbium Doped Fiber Amplifier—EDFA) prior to being launched into the next span. However, signal degradation due to noise and intra-channel nonlinearity such as dispersion effects increase as the signal propagates through the fiber. Consequently, noise and dispersion degradation become significant limiting factors of the maximum possible signal reach.
Dispersion, also known as Group Velocity Dispersion or Chromatic Dispersion, in single mode fibre at least, occurs as a result of two mechanisms: a) Waveguide dispersion: within a single mode fibre, different wavelengths travel along the fibre at different speeds; and b) Material dispersion: the phase velocity of plane waves in glass varies with wavelength.
For the purposes of the present application, references to “dispersion” shall be understood to mean the sum total of group velocity dispersion effects.
Mathematically, first order dispersion can be defined as the derivative of the time delay of the optical path with respect to wavelength. The effect of dispersion can be measured in, for example, picoseconds arrival time spread per nanometer ‘line width’ per kilometer length (ps nm-1 km-1). The magnitude of waveguide and material dispersions both vary with wavelength, and at some wavelengths the two effects act in opposite senses. The amount of dispersion present in a link can also vary with the temperature of the cable, and if the route is changed (e.g., using optical switches). Dispersion in optical fibre presents serious problems when using light sources whose spectrum is non-ideal, for example broad or multispectral-line, or when high data rates are required (e.g., over 2 GB/s).
For the purposes of analyzing the effects of dispersion, it is convenient to represent an optical communications system using the block diagram of FIG. 1. In this case, the transmitter is represented by an electrical-to-optical converter (E/O) 2 which operates to convert an electrical input signal x(t) into a corresponding optical signal XOPT(w) for transmission to the receiver. The optical fiber span 4, including all concatenated components, is represented by a transfer function H(w), which will normally be complex. The Receiver is represented by an optical-to-electrical converter (O/E) 6 which detects the optical signal YOPT(w) received through the optical fiber span 4, and generates a corresponding output signal y(t). For a linear optical channel, the received optical signal YOPT(w) will nominally be equivalent to the product of XOPT(w) and H(w).
In general, the output signal y(t) represents a distorted version of the input data signal x(t). While it would be highly desirable for H(w)≈1, this is rarely the case in prior art systems. Accordingly, it is frequently necessary to utilize at least some form of compensation, so that the original input data signal x(t) can be detected within the distorted output signal y(t).
One commonly used method of addressing the problem of dispersion in high-bandwidth communications systems is by inserting one or more optical dispersion compensators 8, represented in FIG. 1b by the compensation function C(w), within the link Such dispersion compensators may, for example, take the form of length of fibre, a Mach Zehnder interferometer, an optical resonator, or a Bragg reflector. Some of these compensators can also produce a controllable amount of compensation, which enables mitigation of time-variant dispersion effects. In either case, these compensators are intended to at least partially offset the signal distortions introduced by the system transfer function H(w). The compensation function C(w) is a dispersive function that is selected to optimize performance of the link. In a fully linear system, the compensation function C(w) would preferably be equivalent to the complex conjugate H*(w) of the transfer function H(w), in which case H(w)*C(w)=1, and the combined effect of H(w) and C(w)=H*(w) would be an undistorted received signal YOPT(w) that exactly corresponds to the original optical signal XOPT(w). However, limitations of optical components, and the time-varying amount of compensation required, make this objective very difficult to achieve. Additionally, optical compensators are expensive and introduce significant optical losses. These losses must be offset by means of additional optical gain which introduces more optical noise. The additional (or higher performance) optical amplifiers required to provide this increased gain further increases the total cost of the communications system. In addition, the presence of optical dispersion compensators and high performance amplifiers distributed along the length of the link provides a significant technical barrier to system evolution. For example, implementation of optical switching (e.g., at the Tx and/or Rx ends of the link, or an intermediate site without electrical termination) necessarily requires adjustment of optical amplifiers, in order to accommodate changing energy states within the link.
These problems can be alleviated by moving the compensation function to the terminal ends (e.g., the transmitter 2 and/or receiver 6) of the link. This technique typically involves “preprocessing” the input signal x(t) at the transmitter (Tx) end of the link 4 to improve dispersion tolerance, and/or processing the output signal y(t) detected at the receiver (Rx) end of the link to accurately detect the input signal x(t) within the distorted output signal y(t).
For example, high bandwidth traffic can be distributed over a larger number of lower-rate channels. The reduced bit-rate of each channel enhances the dispersion tolerance in proportion to the square of the reduction in the bit-rate. However, this approach is expensive, spectrally inefficient, and creates wave mixing problems.
Dispersion tolerance can be increased by narrowing the spectrum of the transmitted optical signal. Various known techniques may be used for this purpose, such as multilevel coding. However, this requires expensive electronics and significantly reduces the noise tolerance of the communications system.
Subcarrier multiplexing, which involves transmitting a plurality of lower bit-rate signals over one optical carrier, is another known method of increasing dispersion tolerance. In this case, the dispersion tolerance obtained is equivalent to that of the lower bit-rate subcarrier. However this approach is not cost effective and does not have a good noise tolerance.
It is known that the use of a coherent receiver enables the signal degradation due to dispersion to be removed via linear electrical filtering. However, because of their high cost, very few coherent optical receivers have been installed, and the cost of replacing installed receivers with the high performance coherent receivers is prohibitive.
While modulator non-linearity can be compensated, the output signal y(t) detected at the Rx end of the communications system contains distortion components due to non-linearities in both the modulator (transmitter) 2 and the receiver 6, as well due to optical dispersion within the link 4. These distortions are compounded, one upon the other, and it is difficult to distinguish distortions of the output signal y(t) due to non-linearity of the modulator 2 or the receiver 6. It is also difficult to distinguish these effects from dispersion.
Recently, it has been discovered that optical dispersion imposed on a communications signal conveyed through an optical communications system can be compensated by modulating the communications signal in the electrical domain. A compensation function is determined that mitigates the chromatic dispersion. The communications signal is then modulated in the electrical domain using the compensation function. It has been shown that compensation can be implemented in the transmitter, using a look-up-table and digital-to-analog converter to generate an electrical predistorted signal. The electrical predistorted signal is then used to modulate an optical source to generate a corresponding predistorted optical signal for transmission through the optical communications system. Such a system is described in U.S. Pat. No. 7,382,984, belonging to Nortel Networks Limited.
Some of the approaches that have been suggested to compensate for optical dispersion within an optical link require impractically complex digital signal processing at high link dispersions. Some approaches have proposed a solution based on a nonlinear lookup table built into a digital signal processing (DSP) chip. While this solution is effective at low to moderate chromatic dispersion, a large lookup table populated with values resulting from complex calculations based on many measured link parameters would be required for high levels of chromatic dispersion compensation.
Improved techniques are needed to implement electrical domain compensation in a DSP to compensate for high levels of dispersion (e.g., over long fibre lengths).